Some basic Lommel polynomials (Q1283908)

The basic Lommel polynomials associated to the \({}_1\varphi_1\) \(q\)-Bessel function and the Jackson \(q\)-Bessel function are considered as orthogonal polynomials in \(q^\nu\), where \(\nu\) is the order of the corresponding basic Bessel functions. An explicit orthogonality measure which is discrete and unbounded is derived by using the techniques of Chihara and Maki. Some results on the zeros of basic Bessel functions, both as functions of the order and the argument are established. Precise asymptotic behaviour of the zeros of the \({}_1\varphi_1\) \(q\)-Bessel function is also obtained.